Geometric Origin of the Yang-Mills Mass Gap via Conditional Lattice Regularity

Geometric Origin of the Yang-Mills Mass Gap via Conditional Lattice Regularity Abstract The Yang-Mills mass gap problem asks why pure non-Abelian gauge theories exhibit a strictly positive excitation gap despite classical scale invariance. We propose that this gap is a consequence of the discrete, finite-state structure of the physical vacuum. Modeling spacetime as a self-dual 24-cell quantum cellular automaton, we formulate Yang-Mills fields as non-Abelian lattice holonomies with gauge group , whose admissible configurations are constrained by lattice geometry and a finite local Hilbert space reflecting bounded information density and causal propagation. We prove a conditional mass gap theorem, showing that for any physically admissible Yang-Mills theory realizable as the continuum limit of such a lattice system, the spectrum above the vacuum is strictly gapped. The mass gap arises from a minimum action threshold enforced by non-Abelian curvature on elementary dual plaquettes. Apparent gapless behavior corresponds to extrapolating the effective continuum description beyond its physical domain of validity.